HMMs for alignments & Sequence pattern discovery I519 Introduction to Bioinformatics

Contents  Motifs –We have seen motifs in regular expression –Profiles & consensus  Motif search –sequence motifs represent critical positions that are conserved in evolution, so search algorithms employing motifs may be used to identify more divergent sequences than methods based on global sequence similarity  PSI-BLAST (similarity search using PSSM, Position Specific Scoring Matrix )  HMM of protein family (a very brief introduction)

Motifs: Profiles and Consensus a G g t a c T t C c A t a c g t Alignment a c g t T A g t a c g t C c A t C c g t a c g G A Profile C G T Consensus A C G T A C G T  Line up the patterns by their start indexes s = (s 1, s 2, …, s t )  Construct matrix profile with frequencies of each nucleotide in columns  Consensus nucleotide in each position has the highest score in column

Profile Representation of Protein Families Aligned DNA sequences can be represented by a 4 ·n profile matrix reflecting the frequencies of nucleotides in every aligned position. Protein family can be represented by a profile representing frequencies of amino acids. Protein family can be represented by a 20·n profile representing frequencies of amino acids.

Profiles and HMMs  HMMs can also be used for aligning a sequence against a profile representing protein family.  A 20·n profile P corresponds to n sequentially linked match states M 1,…,M n in the profile HMM of P.

Multiple Alignments and Protein Family Classification  Multiple alignment of a protein family shows variations in conservation along the length of a protein  Example: after aligning many globin proteins, the biologists recognized that the helices region in globins are more conserved than others.

What are Profile HMMs ?  A Profile HMM is a probabilistic representation of a multiple alignment.  A given multiple alignment (of a protein family) is used to build a profile HMM.  This model then may be used to find and score less obvious potential matches of new protein sequences.

Profile HMM A profile HMM

Building a Profile HMM  Multiple alignment is used to construct the HMM model.  Assign each column to a Match state in HMM. Add Insertion and Deletion state.  Estimate the emission probabilities according to amino acid counts in column. Different positions in the protein will have different emission probabilities.  Estimate the transition probabilities between Match, Deletion and Insertion states  The HMM model gets trained to derive the optimal parameters.

States of Profile HMM  Match states M 1 …M n (plus begin/end states)  Insertion states I 0 I 1 …I n  Deletion states D 1 …D n

Transition Probabilities in Profile HMM  log(a MI )+log(a IM ) = gap initiation penalty  log(a II gap extension penalty  log(a II ) = gap extension penalty

Emission Probabilities in Profile HMM Probabilty of emitting a symbol a at an Probabilty of emitting a symbol a at an insertion state I j : insertion state I j : e Ij (a) = p(a) where p(a) is the frequency of the where p(a) is the frequency of the occurrence of the symbol a in all the occurrence of the symbol a in all the sequences. sequences.

Profile HMM Alignment  Define v M j (i) as the logarithmic likelihood score of the best path for matching x 1..x i to profile HMM ending with x i emitted by the state M j.  v I j (i) and v D j (i) are defined similarly.

Profile HMM Alignment: Dynamic Programming v M j-1 (i-1) + log(a M j-1, M j ) v M j-1 (i-1) + log(a M j-1, M j ) v M j (i) = log (e M j (x i )/p(x i )) + max v I j-1 (i-1) + log(a I j-1, M j ) v D j-1 (i-1) + log(a D j-1, M j ) v D j-1 (i-1) + log(a D j-1, M j ) v M j (i-1) + log(a M j, I j ) v M j (i-1) + log(a M j, I j ) v I j (i) = log (e I j (x i )/p(x i )) + max v I j (i-1) + log(a I j, I j ) v D j (i-1) + log(a D j, I j ) v D j (i-1) + log(a D j, I j )

Paths in Edit Graph and Profile HMM A path through an edit graph and the corresponding path through a profile HMM

Making a Collection of HMM for Protein Families  Use Blast to separate a protein database into families of related proteins  Construct a multiple alignment for each protein family.  Construct a profile HMM model and optimize the parameters of the model (transition and emission probabilities).  Align the target sequence against each HMM to find the best fit between a target sequence and an HMM

Application of Profile HMM to Modeling Globin Proteins  Globins represent a large collection of protein sequences  400 globin sequences were randomly selected from all globins and used to construct a multiple alignment.  Multiple alignment was used to assign an initial HMM  This model then get trained repeatedly with model lengths chosen randomly between 145 to 170, to get an HMM model optimized probabilities.

hmmer package  Tools for making HMMs and for hmmscan  hmmer3 (as fast as blast)

Sequence Pattern (Motif) Discovery  Finding patterns in multiple alignments, or in unaligned sequences  eMotif (a protein pattern database); eBLOCKs  Gibbs and MEME –To infer patterns in unaligned sequences –Gibbs program starts with a fixed pattern length of W and a random set of locations of the pattern in given input sequences (i.e., the initial pattern is random); and then one sequence is selected at a time randomly and an attempt is made to improve its pattern position. –MEME uses many similar concepts, but uses the EM (expectation maximization) method.

Utilization of Multiple Alignments  Residue conservation –Jalview  Subfamilies –SCI-PHY –FunShift

Readings  Chapter 6